Gaussian mixture model clustering with completed likelihood minimum message length criterion

An improved Gaussian mixture model （GMM）- based clustering method is proposed for the difficult case where the true distribution of data is against the assumed GMM. First, an improved model selection criterion, the completed likelihood minimum message length criterion, is derived. It can measure both the goodness-of-fit of the candidate GMM to the data and the goodness-of-partition of the data. Secondly, by utilizing the proposed criterion as the clustering objective function, an improved expectation- maximization （EM） algorithm is developed, which can avoid poor local optimal solutions compared to the standard EM algorithm for estimating the model parameters. The experimental results demonstrate that the proposed method can rectify the over-fitting tendency of representative GMM-based clustering approaches and can robustly provide more accurate clustering results.

Diagnostics in generalized nonlinear models based on maximum L_q-likelihood estimation

In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.

WOMBAT—A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML)

WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http：//agbu. une.edu.au/-kmeyer/wombat.html

Error Modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

Physics-based Modeling and Simulation for Motional Cable Harness Design

The design work of motional cable in products is vital due to the difficulty in estimating the potential issues in current researches.In this paper,a physics-based modeling and simulation method for the motional cable harness design is presented.The model,based on continuum mechanics,is established by analyzing the force of microelement in equilibrium.During the analysis procedure,three coordinate systems：inertial,Frenet and main-axis coordinate systems are used.By variable substitution and dimensionless processing,the equation set is discretized by differential quadrature method and subsequently becomes an overdetermined nonlinear equation set with boundary conditions solved by Levenberg-Marquardt method.With the profile of motional cable harness obtained from the integral of arithmetic solution,a motion simulation system based on＂path＂and＂profile＂as well as the experimental equipments is built.Using the same parameters as input for the simulation and the real cable harness correspondingly,the issue in designing,such as collision,can be easily found by the simulation system.This research obtains a better result which has no potential collisions by redesign,and the proposed method can be used as an accurate and efficient way in motional cable harness design work.

Wave Motion Compensation Scheme and Its Model Tests for the Salvage of An Ancient Sunken Boat

The application of the vertical hoisting jack and wave motion compensation techniques to the salvage of an ancient sunken boat is introduced. The boat is wooden, loaded with cultural relics. It has been immersed at the bottom of the South China Sea for more than 800 years. In order to protect the structure of the boat and the cultural relics inside to the largest extent, an open caisson is used to hold the sunken beat and the silts around before they are raised from the seabed all together as a whole. In the paper, first, the seakeeping model test of the system of the salvage barge and the open caisson is done to determine some important wave response parameters. And then a further experimental study of the ap- plication of the vertical hoisting jack and wave motion compensation scheme to the salvage of the sunken boat is carried out. In the model tests, the techniques of the integrative mechanic-electronic-hydraulic control, wave motion forecast and wave motion compensation are used to minimize the heave motion of the open caisson. The results of the model tests show that the heave motion of the open caisson can be reduced effectively by the use of the present method.

EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

Modeling and Motion Simulation for A Flying-Wing Underwater Glider with A Symmetrical Airfoil

The flying-wing underwater glider (UG), shaped as a blended wing body, is a new type of underwater vehicle and still requires further research. The shape layout and the configuration of the internal actuators of the flying-wing UG are different from those of "legacy gliders" which have revolving bodies, and these two factors strongly affect the dynamic performance of the vehicle. Considering these differences, we propose a new configuration of the internal actuators for the flying-wing UG and treat the flying-wing UG as a multi-body system when establishing its dynamic model. In this paper, a detailed dynamic model is presented using the Newton-Euler method for the flying-wing UG. Based on the full dynamic model, the effect of the internal actuators on the steady gliding motion of vehicle is studied theoretically, and the relationship between the state parameters of the steady gliding motion and the controlled variables is obtained by solving a set of equilibrium equations. Finally, the behaviors of two classical motion modes of the glider are analyzed based on the simulation. The simulation results demonstrate that the motion performance of the proposed flying-wing UG is satisfactory.

Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.

Dynamics model of underwater robot motion control in 6 degrees of freedom

In order to analyze underwater robot control system dynamics features, a system 6-DOF dynamics model was founded. Underwater robot linear and nonlinear hydrodynamics were analyzed by Taylor series, based on general motion equation. Special control system motion equation was deduced by cluster of inertial items and non-inertial items. For program convenience, motion equation matrix format was presented. Experimental principles of screw propellers, rudders and wings were discussed. Experimental data least-square curve fitting, interpolation and their corresponding traditional equation helped us to obtain the whole system dynamic response procedure. A series of simulation experiments show that the dynamics model is correct and reliable. The model can provide theory proof for analyzing underwater robot motion control system physics characters and provide a mathematic model for traditional control method.

EMPIRICAL LIKELIHOOD-BASED INFERENCE IN LINEAR MODELS WITH INTERVAL CENSORED DATA

An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.

Modeling and simulation of a mini AUV in spatial motion

Accurate modeling and simulation of autonomous underwater vehicle （AUV） is essential for autonomous control and maneuverability research. In this paper, a mini AUV- ＂MAUV-Ⅱ＂ was researched and the nonlinear mathematic model of the AUV in spatial motion was derived based on momentum theorem. The forces acting on AUV were resolved to several modules which were expressed in matrix form. Based on the motion model and combined with virtual reality technology, a motion simulation system was constructed. Considering the characteristic of ＂MAUV-Ⅱ ＂, the heading control and depth control were simulated by adopting S-surface control method. A long distance traveling simulation experiment based on target planning was also done. The simulation results show that the ＂MAUV-Ⅱ＂ has good spatial maneuverability, and verify the feasibility and reliability of control software.

EMPIRICAL LIKELIHOOD FOR LINEAR MODELS UNDER m-DEPENDENT ERRORS

In this paper,the empirical likelihood confidence regions for the regression coefficient in a linear model are constructed under m-dependent errors.It is shown that the blockwise empirical likelihood is a good way to deal with dependent samples.

An Integrated Dynamic Model of Ocean Mining System and Fast Simulation of Its Longitudinal Reciprocating Motion

An integrated dynamic model of China＇s deep ocean mining system is developed and the fast simulation analysis of its longitudinal reciprocating motion operation processes is achieved. The seafloor tracked miner is built as a three-dimensional single-body model with six-degree-of-freedom. The track-terrain interaction is modeled by partitioning the track-terrain interface into a certain number of mesh elements with three mutually perpendicular forces, including the normal force, the longitudinal shear force and the lateral shear force, acting on the center point of each mesh element. The hydrodynamic force of the miner is considered and applied. By considering the operational safety and collection efficiency, two new mining paths for the miner on the seafloor are proposed, which can be simulated with the established single-body dynamic model of the miner. The pipeline subsystem is built as a three-dimensional multi-body discrete element model, which is divided into rigid elements linked by flexible connectors. The flexible connector without mass is represented by six spring-damper elements. The external hydrodynamic forces of the ocean current from the longitudinal and lateral directions are both considered and modeled based on the Morison formula and applied to the mass center of each corresponding discrete rigid element. The mining ship is simplified and represented by a general kinematic point, whose heave motion induced by the ocean waves and the longitudinal and lateral towing motions are considered and applied. By integrating the single-body dynamic model of the miner and the multi-body discrete element dynamic model of the pipeline, and defining the kinematic equations of the mining ship, the integrated dynamic model of the total deep ocean mining system is formed. The longitudinal reciprocating motion operation modes of the total mining system, which combine the active straight-line and turning motions of the miner and the ship, and the passive towed motions of the pipeline, are proposed and simulated with the developed 3D dynamic model. Some critical simulation results are obtained and analyzed, such as the motion trajectories of key subsystems, the velocities of the buoyancy modules and the interaction forces between subsystems, which in a way can provide important theoretical basis and useful technical reference for the practical deep ocean mining system analysis, operation and control.

IN-PLANE WAVE MOTION IN FINITE ELEMENT MODEL

The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.

Development of an aftershock occurrence model calibrated for Turkey and the resulting likelihoods

This paper presents the calibration of Omori’s aftershock occurrence rate model for Turkey and the resulting likelihoods. Aftershock occurrence rate models are used for estimating the probability of an aftershock that exceeds a specific magnitude threshold within a time interval after the mainshock. Critical decisions on the post-earthquake safety of structures directly depend on the aftershock hazard estimated using the occurrence model. It is customary to calibrate models in a region-specific manner. These models depend on rate parameters(a, b, c and p) related to the seismicity characteristics of the investigated region. In this study, the available well-recorded aftershock sequences for a set of Mw ≥ 5.9 mainshock events that were observed in Turkey until 2012 are considered to develop the aftershock occurrence model. Mean estimates of the model parameters identified for Turkey are a =-1.90, b = 1.11, c = 0.05 and p = 1.20. Based on the developed model, aftershock likelihoods are computed for a range of different time intervals and mainshock magnitudes. Also, the sensitivity of aftershock probabilities to the model parameters is investigated. Aftershock occurrence probabilities estimated using the model are expected to be useful for post-earthquake safety evaluations in Turkey.

Vehicle Motion Prediction at Intersections Based on the Turning Intention and Prior Trajectories Model

Intersections are quite important and complex traffic scenarios,where the future motion of surrounding vehicles is an indispensable reference factor for the decision-making or path planning of autonomous vehicles.Considering that the motion trajectory of a vehicle at an intersection partly obeys the statistical law of historical data once its driving intention is determined,this paper proposes a long short-term memory based(LSTM-based)framework that combines intention prediction and trajectory prediction together.First,we build an intersection prior trajectories model(IPTM)by clustering and statistically analyzing a large number of prior traffic flow trajectories.The prior trajectories model with fitted probabilistic density is used to approximate the distribution of the predicted trajectory,and also serves as a reference for credibility evaluation.Second,we conduct the intention prediction through another LSTM model and regard it as a crucial cue for a trajectory forecast at the early stage.Furthermore,the predicted intention is also a key that is associated with the prior trajectories model.The proposed framework is validated on two publically released datasets,next generation simulation(NGSIM)and INTERACTION.Compared with other prediction methods,our framework is able to sample a trajectory from the estimated distribution,with its accuracy improved by about 20%.Finally,the credibility evaluation,which is based on the prior trajectories model,makes the framework more practical in the real-world applications.

Motion/Posture Modeling and Simulation Verification of Physically Handicapped in Manufacturing System Design

Non-obstacle design is critical to tailor physically handicapped workers in manufacturing system. Simultaneous consideration of variability in physically disabled users, machines and environment of the manufacturing system is extremely complex and generally requires modeling of physically handicapped interaction with the system. Most current modeling either concentrates on the task results or functional disability. The integration of physical constraints with task constraints is far more complex because of functional disability and its extended influence on adjacent body parts. A framework is proposed to integrate the two constraints and thus model the specific behavior of the physical handicapped in virtual environment generated by product specifications. Within the framework a simplified model of physical disabled body is constructed, and body motion is generated based on 3 levels of constraints（effecter constraints, kinematics constraints and physical constraints）. The kinematics and dynamic calculations are made and optimized based on the weighting manipulated by the kinematics constraints and dynamic constraints. With object transferring task as example, the model is validated in Jack 6.0. Modelled task motion elements except for squatting and overreaching well matched with captured motion elements. The proposed modeling method can model the complex behavior of the physically handicapped by integrating both task and physical disability constraints.

NONLINEAR MOTION MECHANICS MODEL OF CURVED BLOOD VESSEL

A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This model includes much more physiological factors. It couples the interaction of blood flow with mechanical factors such as the displacement, deformation, strain and stress etc. of the curved blood vessel. It is of great importance for investigating the circulation rules of the cardiovascular system and the nonlinear pulse wave propagation in curved blood vessels.

Lg-Q model and its implication on high-frequency ground motion for earthquakes in the Sichuan and Yunnan region

Low-rise buildings are susceptible to high-frequency ground motion.The high-frequency ground motions at regional distances are mainly controlled by crustal Lg waves whose amplitudes are typically much larger than those of body waves.In this study,we develop a Lg-wave Q model for the Sichuan and Yunnan region in the frequency band of 0.3–2.0 Hz using regional seismic records of 1166 earthquakes recorded at 152 stations.Comparison between the observed pattern of ground motion from real earthquake and model prediction demonstrates the robustness and effectiveness of our Lg-Q model.Then,assuming that the Lg-wave Q structure is the main factor affecting the propagation of the high-frequency ground motions,we calculate the spatial distributions of high-frequency ground motions from scenario earthquakes at different locations in the region using the average Lg-wave attenuation model over the frequency band of 0.3–2.0 Hz.We also use the Lg-Q model to estimate the distribution of cumulative energy of high-frequency ground motions based on the historical seismicity of the Sichuan and Yunnan region.Results show that the Lg-Q model can be used effectively in estimating the spatial distribution of high-frequency seismic energies and thus can contribute to the assessment of seismic hazard to low-rise buildings.